Year: 2016
Author: Jing Chang
Communications in Mathematical Research , Vol. 32 (2016), Iss. 4 : pp. 289–302
Abstract
In this paper, the Dirichlet boundary value problems of the nonlinear beam equation $u_{tt} + ∆^2u + αu + ϵϕ(t)(u + u^3 ) = 0, α > 0$ in the dimension one is considered, where $u(t, x)$ and $ϕ(t$) are analytic quasi-periodic functions in $t$, and $ϵ$ is a small positive real-number parameter. It is proved that the above equation admits a small-amplitude quasi-periodic solution. The proof is based on an infinite dimensional KAM iteration procedure.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2016.04.01
Communications in Mathematical Research , Vol. 32 (2016), Iss. 4 : pp. 289–302
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: beam equation infinite dimension Hamiltonian system KAM theory reducibility.